SIAM Journal on Numerical Analysis · 1985 · 39 citations · 6 references
Natural SciencesMathematicsComputational MechanicsDifferential EquationsDynamical SystemsEigenvalue ProblemsLinear AlgebraMatrix ComputationNumerical Linear AlgebraSpectral TheorySystems Of Differential EquationsEigenvalue AlgorithmsEigenvalue ComputationLax PairsMatrix Eigenvalue ProblemsMatrix Equation SolversQr DecompositionSpectral Asymptotics
In this paper we consider a variety of isospectral flows on the set of $n \times n$ matrices. These flows arise from Lax pairs and can all be interpreted in terms of the $QR$ decomposition for nonsingular matrices. The asymptotics of these differential equations are considered in detail and for symmetric matrices these asymptotics provide a new method of solving the eigenvalue problem.
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The Algebraic Eigenvalue Problem
E. I., J. H. Wilkinson · Mathematics of Computation · 1966 · 5.2K citations
The Toda lattice. II. Existence of integrals
H. Flaschka · Physical review. B, Solid state · 1974 · 753 citations